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Grade 12 College

Twelfth Grade (Grade 12) Integrals Questions

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Grade 12 Integrals
What is the area under the curve for the function [math]f(x)=3x^3+2x^2[/math] on the closed interval [math][-5,5][/math]?
  1. [math]int_-5^5(3x^3+2x^2)dx=500/3[/math]
  2. [math]int_-5^5(3x^3+2x^2)dx=3/500[/math]
  3. [math]int_-5^5(3x^3+2x^2)dx=3[/math]
  4. [math]int_-5^5(3x^3+2x^2)dx=500[/math]
Grade 12 Integrals
Find the indefinite integral. [math]int(4x)/(2x^2-1) \ dx[/math]
  1. [math](2x^2-1)^2+C[/math]
  2. [math]ln 2x^2+C[/math]
  3. [math]ln |2x^2-1|+C[/math]
  4. [math]2/(2x^2-1)^2 +C[/math]
Grade 12 Integrals
Find the indefinite integral. [math]intcsc(x^2-2)cot(x^2-2)x \ dx[/math]
  1. [math]1/2tan( x^2-2)+C[/math]
  2. [math] cot(x^2-2)+C[/math]
  3. [math]-1/2csc( x^2-2)+C[/math]
  4. [math]-sec( x^2-2)+C[/math]
Grade 12 Integrals
Find the indefinite integral. [math]intcos^4(x)sin(x) \ dx[/math]
  1. [math]cos^5(x)+C[/math]
  2. [math]-1/5sin^5(x)+C[/math]
  3. [math]sin^5(x)+C[/math]
  4. [math]-1/5cos^5(x)+C[/math]
  5. [math]-5cos^5(x)+C[/math]
Grade 12 Integrals
Find the indefinite integral. [math]inttan(8x)8 \ dx [/math]
  1. [math]-8ln|cos8x|+C[/math]
  2. [math]ln|sec8x|+C[/math]
  3. [math]1/8ln|cos8x|+C[/math]
  4. [math]-ln|cos8x|+C[/math]
Grade 12 Integrals
Find the indefinite integral. [math]intcot(3x^4+5)12x^3 \ dx[/math]
  1. [math]ln|sin3x^4|+C[/math]
  2. [math]ln|sin(3x^4+5)|+C[/math]
  3. [math]ln|sin12x^3|+C[/math]
  4. [math]ln|sin(12x^3+5)|+C[/math]
Grade 12 Integrals
Find the indefinite integral. [math]int(5)/(cos5x) \ dx[/math]
  1. [math]ln|sec5x+tan5x|+C[/math]
  2. [math]ln|csc5x+cot5x|+C[/math]
  3. [math]ln|tan5x|+C[/math]
  4. [math]ln|sec5x|+C[/math]
Grade 12 Integrals
What is the indefinite integral of [math]f(x)=3x^3+2x^2[/math]?
  1. [math]int3x^3+2x^2 dx = (3x^4)/4+(2x^3)/3+C[/math]
  2. [math]int3x^3+2x^2 dx = 9x^2+4x+C[/math]
  3. [math]int3x^3+2x^2 dx = 3x^3+2x^2+C[/math]
  4. [math]int3x^3+2x^2 dx = (4x^3)/3+(3x^2)/2+C[/math]
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